tLaSDI: Thermodynamics-informed latent space dynamics identification

• URL: http://arxiv.org/abs/2403.05848v2
• Date: Fri, 22 Mar 2024 01:01:58 GMT
• Title: tLaSDI: Thermodynamics-informed latent space dynamics identification
• Authors: Jun Sur Richard Park, Siu Wun Cheung, Youngsoo Choi, Yeonjong Shin,
• Abstract summary: We propose a latent space dynamics identification method, namely tLa, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. An intriguing correlation is empirically observed between a quantity from tLa in the latent space and the behaviors of the full-state solution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

Related papers

• No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs [56.78271181959529]
  This paper proposes a conceptual shift to modeling low-dimensional dynamical systems by departing from the traditional two-step modeling process. Instead of first discovering a closed-form equation and then analyzing it, our approach, direct semantic modeling, predicts the semantic representation of the dynamical system. Our approach not only simplifies the modeling pipeline but also enhances the transparency and flexibility of the resulting models.
  arXiv  Detail & Related papers  (2025-01-30T18:36:48Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs) We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• Parametric Taylor series based latent dynamics identification neural networks [0.3139093405260182]
  A new latent identification of nonlinear dynamics, P-TLDINets, is introduced. It relies on a novel neural network structure based on Taylor series expansion and ResNets.
  arXiv  Detail & Related papers  (2024-10-05T15:10:32Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• NeuralODEs for VLEO simulations: Introducing thermoNET for Thermosphere Modeling [4.868863044142366]
  thermoNET represents thermospheric density in satellite orbital propagation using a reduced amount of differentiable computations. Network parameters are learned based on observed dynamics, adapting through ODE sensitivities.
  arXiv  Detail & Related papers  (2024-05-29T09:12:44Z)
• Thermodynamics-informed super-resolution of scarce temporal dynamics data [4.893345190925178]
  We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution. Our method uses adversarial autoencoders, which reduce the dimensionality of the full order model to a set of latent variables that are enforced to match a prior. A second neural network is trained to learn the physical structure of the latent variables and predict their temporal evolution.
  arXiv  Detail & Related papers  (2024-02-27T13:46:45Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs [3.4527210650730393]
  We investigate employing deep autoencoders for discovering the reduced basis representation. Test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system.
  arXiv  Detail & Related papers  (2021-07-06T17:45:37Z)
• Deep learning of thermodynamics-aware reduced-order models from data [0.08699280339422537]
  We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system. We then predict its time evolution using thermodynamically-consistent deep neural networks.
  arXiv  Detail & Related papers  (2020-07-03T08:49:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.